midterm2 solution - Chem 442 Fall 2010 Second Hour Exam...

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Unformatted text preview: Chem 442 Fall 2010 Second Hour Exam Answers 1) (30 points) This is a perturbation theory question, similar to the perturbed H. O. one described in class. It uses explicit matrices. The Hamiltonian matrix of the unperturbed Hamiltonian is = 500 400 60 50 H thus giving five unperturbed states of energies 0, 60, 60, 400 and 500 ( in wavenumber units). The perturbation Hamiltonian is = 10 30 10 10 30 5 10 5 1 i i H , again in wavenumbers. Calculate the perturbed energies of all five states and state whether each one was changed by a first order or a second order perturbation, or both. State 1 E perturbed = - 2.166666666 2nd only State 2 E perturbed = 48.5 2nd only State 3 E perturbed = 61.66666666 2nd only State 4 E perturbed = 410 1st only State 5 E perturbed = 512 both 2) (30 points) The expectation value of the energy of some Hamiltonian and some (unnormalized) trial wavefunction is d d H E = * * where d and the integration limits are appropriate to the problem. The numerator is called a Hamiltonian integral and the denominator is a normalization integral. Variational theory minimizes this to get an approximate value for the ground state energy of the system....
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midterm2 solution - Chem 442 Fall 2010 Second Hour Exam...

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